A055664 -id:A055664 - cp's OEIS frontend

A341786 Norms of prime ideals in Z[(1+sqrt(-15))/2], the ring of integers of Q(sqrt(-15)).

2, 3, 5, 17, 19, 23, 31, 47, 49, 53, 61, 79, 83, 107, 109, 113, 121, 137, 139, 151, 167, 169, 173, 181, 197, 199, 211, 227, 229, 233, 241, 257, 263, 271, 293, 317, 331, 347, 349, 353, 379, 383, 409, 421, 439, 443, 467, 499, 503, 541, 557, 563, 571, 587

Offset: 1

Jianing Song, Feb 19 2021

The norm of a nonzero ideal I in a ring R is defined as the size of the quotient ring R/I.
Note that Z[(1+sqrt(-15))/2] has class number 2.
Consists of the primes congruent to 1, 2, 3, 4, 5, 8 modulo 15 and the squares of primes congruent to 7, 11, 13, 14 modulo 15.
For primes p == 1, 4 (mod 15), there are two distinct ideals with norm p in Z[(1+sqrt(-15))/2], namely (x + y*(1+sqrt(-15))/2) and (x + y*(1-sqrt(-15))/2), where (x,y) is a solution to x^2 + x*y + 4*y^2 = p; for p == 2, 8 (mod 15), there are also two distinct ideals with norm p, namely (p, x + y*(1+sqrt(-15))/2) and (p, x + y*(1-sqrt(-15))/2), where (x,y) is a solution to x^2 + x*y + 4*y^2 = p^2 with y != 0; (3, sqrt(-15)) and (5, sqrt(-15)) are respectively the unique ideal with norm 3 and 5; for p == 7, 11, 13, 14 (mod 15), (p) is the only ideal with norm p^2.

			Let |I| be the norm of an ideal I, then:
|(2, (1+sqrt(-15))/2)| = |(2, (1-sqrt(-15))/2)| = 2;
|(3, sqrt(-15))| = 3;
|(5, sqrt(-15))| = 5;
|(17, 7+4*sqrt(-15))| = |(17, 7-4*sqrt(-15))| = 17;
|(2 + sqrt(-15))| = |(2 - sqrt(-15))| = 19;
|(23, 17+4*sqrt(-15))| = |(23, 17-4*sqrt(-15))| = 23;
|(4 + sqrt(-15))| = |(4 - sqrt(-15))| = 31.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A316569, A033212, A106859, A191018, A191062.
The number of distinct ideals with norm n is given by A035175.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), this sequence (D=-15*), A341787 (D=-19), A091727 (D=-20*), A341788 (D=-43), A341789 (D=-67), A341790 (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.

isA341786(n) = my(disc=-15); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)

A341787 Norms of prime elements in Z[(1+sqrt(-19))/2], the ring of integers of Q(sqrt(-19)).

Original entry on oeis.org

4, 5, 7, 9, 11, 17, 19, 23, 43, 47, 61, 73, 83, 101, 131, 137, 139, 149, 157, 163, 169, 191, 197, 199, 229, 233, 239, 251, 263, 271, 277, 283, 311, 313, 347, 349, 353, 359, 367, 389, 397, 419, 443, 457, 461, 463, 467, 479, 491, 499, 503, 541, 557, 571

Offset: 1

Jianing Song, Feb 19 2021

Also norms of prime ideals in Z[(1+sqrt(-19))/2], which is a unique factorization domain. The norm of a nonzero ideal I in a ring R is defined as the size of the quotient ring R/I.
Consists of the primes such that (p,19) >= 0 and the squares of primes such that (p,19) = -1, where (p,19) is the Legendre symbol.
For primes p such that (p,19) = 1, there are two distinct ideals with norm p in Z[(1+sqrt(-19))/2], namely (x + y*(1+sqrt(-19))/2) and (x + y*(1-sqrt(-19))/2), where (x,y) is a solution to x^2 + x*y + 5*y^2 = p; for p = 19, (sqrt(-19)) is the unique ideal with norm p; for primes p with (p,19) = -1, (p) is the only ideal with norm p^2.

			norm((1 + sqrt(-19))/2) = norm((1 - sqrt(-19))/2) = 5;
norm((3 + sqrt(-19))/2) = norm((3 - sqrt(-19))/2) = 7;
norm((5 + sqrt(-19))/2) = norm((5 - sqrt(-19))/2) = 11;
norm((7 + sqrt(-19))/2) = norm((7 - sqrt(-19))/2) = 17.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A011585, A106863, A191019, A191063.
The number of nonassociative elements with norm n (also the number of distinct ideals with norm n) is given by A035171.
The total number of elements with norm n is given by A028641.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), A341786 (D=-15*), this sequence (D=-19), A091727 (D=-20*), A341788 (D=-43), A341789 (D=-67), A341790 (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.

isA341787(n) = my(disc=-19); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)

A341788 Norms of prime elements in Z[(1+sqrt(-43))/2], the ring of integers of Q(sqrt(-43)).

Original entry on oeis.org

4, 9, 11, 13, 17, 23, 25, 31, 41, 43, 47, 49, 53, 59, 67, 79, 83, 97, 101, 103, 107, 109, 127, 139, 167, 173, 181, 193, 197, 229, 239, 251, 269, 271, 281, 283, 293, 307, 311, 317, 337, 353, 359, 361, 367, 379, 397, 401, 431, 439, 443, 461, 479, 487, 509

Offset: 1

Jianing Song, Feb 19 2021

Also norms of prime ideals in Z[(1+sqrt(-43))/2], which is a unique factorization domain. The norm of a nonzero ideal I in a ring R is defined as the size of the quotient ring R/I.
Consists of the primes such that (p,43) >= 0 and the squares of primes such that (p,43) = -1, where (p,43) is the Legendre symbol.
For primes p such that (p,43) = 1, there are two distinct ideals with norm p in Z[(1+sqrt(-43))/2], namely (x + y*(1+sqrt(-43))/2) and (x + y*(1-sqrt(-43))/2), where (x,y) is a solution to x^2 + x*y + 11*y^2 = p; for p = 43, (sqrt(-43)) is the unique ideal with norm p; for primes p with (p,43) = -1, (p) is the only ideal with norm p^2.

			norm((1 + sqrt(-43))/2) = norm((1 - sqrt(-43))/2) = 11;
norm((3 + sqrt(-43))/2) = norm((3 - sqrt(-43))/2) = 13;
norm((5 + sqrt(-43))/2) = norm((5 - sqrt(-43))/2) = 17;
norm((7 + sqrt(-43))/2) = norm((7 - sqrt(-43))/2) = 23;
...
norm((19 + sqrt(-43))/2) = norm((19 - sqrt(-43))/2) = 101.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A011591, A106891, A191031, A184902.
The number of nonassociative elements with norm n (also the number of distinct ideals with norm n) is given by A035147.
The total number of elements with norm n is given by A138811.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), A341786 (D=-15*), A341787 (D=-19), A091727 (D=-20*), this sequence (D=-43), A341789 (D=-67), A341790 (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.

isA341788(n) = my(disc=-43); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)

A341789 Norms of prime elements in Z[(1+sqrt(-67))/2], the ring of integers of Q(sqrt(-67)).

Original entry on oeis.org

4, 9, 17, 19, 23, 25, 29, 37, 47, 49, 59, 67, 71, 73, 83, 89, 103, 107, 121, 127, 131, 149, 151, 157, 163, 167, 169, 173, 181, 193, 199, 211, 223, 227, 241, 257, 263, 269, 277, 283, 293, 307, 317, 349, 359, 389, 397, 419, 421, 431, 439, 449, 457, 461

Offset: 1

Jianing Song, Feb 19 2021

Also norms of prime ideals in Z[(1+sqrt(-67))/2], which is a unique factorization domain. The norm of a nonzero ideal I in a ring R is defined as the size of the quotient ring R/I.
Consists of the primes such that (p,67) >= 0 and the squares of primes such that (p,67) = -1, where (p,67) is the Legendre symbol.
For primes p such that (p,67) = 1, there are two distinct ideals with norm p in Z[(1+sqrt(-67))/2], namely (x + y*(1+sqrt(-67))/2) and (x + y*(1-sqrt(-67))/2), where (x,y) is a solution to x^2 + x*y + 17*y^2 = p; for p = 67, (sqrt(-67)) is the unique ideal with norm p; for primes p with (p,67) = -1, (p) is the only ideal with norm p^2.

			norm((1 + sqrt(-67))/2) = norm((1 - sqrt(-67))/2) = 17;
norm((3 + sqrt(-67))/2) = norm((3 - sqrt(-67))/2) = 19;
norm((5 + sqrt(-67))/2) = norm((5 - sqrt(-67))/2) = 23;
norm((7 + sqrt(-67))/2) = norm((7 - sqrt(-67))/2) = 29;
...
norm((31 + sqrt(-67))/2) = norm((31 - sqrt(-67))/2) = 257.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A011596, A106933, A191041, A191077.
The number of nonassociative elements with norm n (also the number of distinct ideals with norm n) is given by A318982.
The total number of elements with norm n is given by A318984.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), A341786 (D=-15*), A341787 (D=-19), A091727 (D=-20*), A341788 (D=-43), this sequence (D=-67), A341790 (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.

isA341783(n) = my(disc=-67); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)

A341790 Norms of prime elements in Z[(1+sqrt(-163))/2], the ring of integers of Q(sqrt(-163)).

Original entry on oeis.org

4, 9, 25, 41, 43, 47, 49, 53, 61, 71, 83, 97, 113, 121, 131, 151, 163, 167, 169, 173, 179, 197, 199, 223, 227, 251, 263, 281, 289, 307, 313, 347, 359, 361, 367, 373, 379, 383, 397, 409, 419, 421, 439, 457, 461, 487, 499, 503, 523, 529, 547, 563, 577, 593

Offset: 1

Jianing Song, Feb 19 2021

Also norms of prime ideals in Z[(1+sqrt(-163))/2], which is a unique factorization domain. The norm of a nonzero ideal I in a ring R is defined as the size of the quotient ring R/I.
Consists of the primes such that (p,163) >= 0 and the squares of primes such that (p,163) = -1, where (p,163) is the Legendre symbol.
For primes p such that (p,163) = 1, there are two distinct ideals with norm p in Z[(1+sqrt(-163))/2], namely (x + y*(1+sqrt(-163))/2) and (x + y*(1-sqrt(-163))/2), where (x,y) is a solution to x^2 + x*y + 41*y^2 = p; for p = 163, (sqrt(-163)) is the unique ideal with norm p; for primes p with (p,163) = -1, (p) is the only ideal with norm p^2.

			norm((1 + sqrt(-163))/2) = norm((1 - sqrt(-163))/2) = 41;
norm((3 + sqrt(-163))/2) = norm((3 - sqrt(-163))/2) = 43;
norm((5 + sqrt(-163))/2) = norm((5 - sqrt(-163))/2) = 47;
norm((7 + sqrt(-163))/2) = norm((7 - sqrt(-163))/2) = 53;
...
norm((79 + sqrt(-163))/2) = norm((79 - sqrt(-163))/2) = 1601.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A011615, A257362, A296921, A296915.
The number of nonassociative elements with norm n (also the number of distinct ideals with norm n) is given by A318983.
The total number of elements with norm n is given by A318985.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), A341786 (D=-15*), A341787 (D=-19), A091727 (D=-20*), A341788 (D=-43), A341789 (D=-67), this sequence (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.

isA341783(n) = my(disc=-163); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)

A341783 Absolute values of norms of prime elements in Z[(1+sqrt(5))/2], the ring of integers of Q(sqrt(5)).

Original entry on oeis.org

4, 5, 9, 11, 19, 29, 31, 41, 49, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 169, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 289, 311, 331, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 449, 461, 479, 491, 499, 509, 521, 529

Offset: 1

Jianing Song, Feb 19 2021

Also norms of prime ideals in Z[(1+sqrt(5))/2], which is a unique factorization domain. The norm of a nonzero ideal I in a ring R is defined as the size of the quotient ring R/I.
Consists of the primes congruent to 0, 1, 4 modulo 5 and the squares of primes congruent to 2, 3 modulo 5.
For primes p == 1, 4 (mod 5), there are two distinct ideals with norm p in Z[(1+sqrt(5))/2], namely (x + y*(1+sqrt(5))/2) and (x + y*(1-sqrt(5))/2), where (x,y) is a solution to x^2 + x*y - y^2 = p; for p = 5, (sqrt(5)) is the unique ideal with norm p; for p == 2, 3 (mod 5), (p) is the only ideal with norm p^2.

			norm((7 + sqrt(5))/2) = norm((7 - sqrt(5))/2) = 11;
norm((9 + sqrt(5))/2) = norm((9 - sqrt(5))/2) = 19;
norm((11 + sqrt(5))/2) = norm((11 - sqrt(5))/2) = 29;
norm(6 + sqrt(5)) = norm(6 - sqrt(5)) = 31.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A080891, A038872, A045468, A003631.
The number of nonassociative elements with absolute value of norm n (also the number of distinct ideals with norm n) is given by A035187.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), this sequence (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), A341786 (D=-15*), A341787 (D=-19), A091727 (D=-20*), A341788 (D=-43), A341789 (D=-67), A341790 (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.

isA341783(n) = my(disc=5); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)

A055667 Number of Eisenstein-Jacobi primes of norm n.

Original entry on oeis.org

0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0

Offset: 0

N. J. A. Sloane, Jun 09 2000

These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2.

			There are 6 Eisenstein-Jacobi primes of norm 3, omega-omega^2 times one of the 6 units [ +-1, +-omega, +-omega^2 ] but only one up to equivalence.

R. K. Guy, Unsolved Problems in Number Theory, A16.
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VI.

Cf. A055664-A055668, A055025-A055029, A135461, A135462. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice.

a[3] = 6; a[p_ /; PrimeQ[p] && Mod[p, 6] == 1] = 12; a[n_ /; PrimeQ[p = Sqrt[n]] && Mod[p, 3] == 2] = 6; a[] = 0; Table[a[n], {n, 0, 99}] (* _Jean-François Alcover, Oct 24 2013, after Franklin T. Adams-Watters *)

a(n) = 6 * A055668(n). - Franklin T. Adams-Watters, May 05 2006

More terms from Franklin T. Adams-Watters, May 05 2006

A055668 Number of inequivalent Eisenstein-Jacobi primes of norm n.

Original entry on oeis.org

0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0

Offset: 0

N. J. A. Sloane, Jun 09 2000

These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2.

Two primes are considered equivalent if they differ by multiplication by a unit (+-1, +-omega, +-omega^2).

			There are 6 Eisenstein-Jacobi primes of norm 3, omega-omega^2 times one of the 6 units [ +-1, +-omega, +-omega^2 ] but only one up to equivalence.

R. K. Guy, Unsolved Problems in Number Theory, A16.
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VI.

Cf. A055664-A055667, A055025-A055029. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice.

a[3] = 1; a[p_ /; PrimeQ[p] && Mod[p, 6] == 1] = 2; a[n_ /; PrimeQ[p = Sqrt[n]] && Mod[p, 3] == 2] = 1; a[] = 0; Table[a[n], {n, 0, 104}] (* _Jean-François Alcover, Aug 19 2013, after Franklin T. Adams-Watters *)
Table[Which[PrimeQ[n]&&Mod[n,6]==1,2,n==3,1,PrimeQ[Sqrt[n]]&&Mod[ Sqrt[ n],3] == 2,1,True,0],{n,0,110}] (* Harvey P. Dale, Jun 17 2017 *)

a(n) = 2 if n is a prime = 1 (mod 6); a(n) = 1 if n = 3 or n = p^2 where p is a prime = 2 (mod 3); a(n) = 0 otherwise. - Franklin T. Adams-Watters, May 05 2006

More terms from Franklin T. Adams-Watters, May 05 2006

A055026 Number of Gaussian primes of successive norms (indexed by A055025).

Original entry on oeis.org

4, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8

Offset: 1

N. J. A. Sloane, Jun 09 2000

These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).

			There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).

R. K. Guy, Unsolved Problems in Number Theory, A16.
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. V.

Index entries for Gaussian integers and primes

Cf. A055025-A055029, A055664-...

m = 32; Length /@ Split[Sort[Select[Flatten[Table[{a^2 + b^2, a + b*I}, {a, -m, m}, {b, -m, m}], 1], PrimeQ[#[[2]], GaussianIntegers -> True] & ]], #1[[1]] == #2[[1]] & ][[1 ;; 87]] (* Jean-François Alcover, Apr 08 2011 *)

More terms from Reiner Martin, Jul 20 2001

A055027 Number of inequivalent Gaussian primes of successive norms (indexed by A055025).

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2

Offset: 1

N. J. A. Sloane, Jun 09 2000

These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).

Two primes are considered equivalent if they differ by multiplication by a unit (+-1, +-i).

			There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).

R. K. Guy, Unsolved Problems in Number Theory, A16.
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. V.

Index entries for Gaussian integers and primes

Cf. A055025-A055029, A055664-...

norms = Union[ #*Conjugate[#]& [ Select[ Flatten[ Table[a + b*I, {a, 0, 31}, {b, 0, 31}]], PrimeQ[#, GaussianIntegers -> True] &]]]; f[norm_] := (Clear[a, b]; primes = {a + b*I} /. {ToRules[ Reduce[a^2 + b^2 == norm, {a, b}, Integers]]}; primes //. {p1___, p2_, p3___, p4_, p5___} /; MatchQ[p2, (-p4 | I*p4 | -I*p4)] :> {p1, p2, p3, p5} // Length); A055027 = f /@ norms (* Jean-François Alcover, Nov 30 2012 *)

More terms from Reiner Martin, Jul 20 2001

cp's OEIS Frontend

A341786 Norms of prime ideals in Z[(1+sqrt(-15))/2], the ring of integers of Q(sqrt(-15)).

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A341787 Norms of prime elements in Z[(1+sqrt(-19))/2], the ring of integers of Q(sqrt(-19)).

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A341788 Norms of prime elements in Z[(1+sqrt(-43))/2], the ring of integers of Q(sqrt(-43)).

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A341789 Norms of prime elements in Z[(1+sqrt(-67))/2], the ring of integers of Q(sqrt(-67)).

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A341790 Norms of prime elements in Z[(1+sqrt(-163))/2], the ring of integers of Q(sqrt(-163)).

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A341783 Absolute values of norms of prime elements in Z[(1+sqrt(5))/2], the ring of integers of Q(sqrt(5)).

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A055667 Number of Eisenstein-Jacobi primes of norm n.

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A055668 Number of inequivalent Eisenstein-Jacobi primes of norm n.

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